To cite this version:Mourad Baïou, Fancisco Barahona. A linear programming approach to increasing the weight of all minimum spanning trees. CECO-889. 2005 Abstract:Given a graph where increasing the weight of an edge has a nondecreasing convex piecewise linear cost, we study the problem of finding a minimum cost increase of the weights so that the value of all minimum spanning trees is equal to some target value. We formulate this as a combinatorial linear program and give an algorithm. Mots clés :Arbres couvrants de poids minimum, sécurisation des réseaux.Key Words : Minimum weight spanning trees, packing spanning trees, network reinforcement, strength problem.y Classification AMS:1 Laboratoire d'Econométrie, CNRS et Ecole polytechnique. A LINEAR PROGRAMMING APPROACH TO INCREASING THE WEIGHT OF ALL MINIMUM SPANNING TREESMOURAD BAÏOU AND FRANCISCO BARAHONA Abstract. Given a graph where increasing the weight of an edge has a nondecreasing convex piecewise linear cost, we study the problem of finding a minimum cost increase of the weights so that the value of all minimum spanning trees is equal to some target value. We formulate this as a combinatorial linear program and give an algorithm.